The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.

中文翻译：

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湍流预混火焰随机场模拟的分辨率要求

在湍流预混燃烧模拟的背景下研究了随机场概率密度函数方法的空间分辨率要求。随机场方法是将传输概率密度函数建模框架实施到湍流燃烧大涡模拟中的一种有吸引力的方法。在预混燃烧 LES 中，数值网格应该能够解析因随机场方程求解而产生的火焰状结构。通过对自由传播平面湍流预混火焰的随机场模拟分析，表明随机场模拟中的火焰状结构可以比 LES 滤波器长度尺度窄几个数量级。对于低卡洛维茨数燃烧，分辨率不足最严重，其中随机场火焰结构的厚度约为层流火焰厚度。然后，通过执行实验室本生火焰的 LES 并比较独立细化网格间距和过滤器长度尺度的效果，评估分辨率对 LES 预测的影响。将 LES 滤波器长度比例设置为等于网格间距的通常做法会导致严重的分辨率不足和火焰的数值增厚，并导致湍流火焰速度出现重大误差。对于涉及高压预混燃烧的许多实际应用来说，精确求解随机场方程所需的数值分辨率是令人望而却步的。这促进了加厚随机场方法的开发（Picciani 等人 Flow Turbul.Combust.X, YYY (2018)），以确保随机场模拟的数值准确性。