The Stochastic Fields approach is an effective way to implement transported Probability Density Function modelling into Large Eddy Simulation of turbulent combustion. In premixed turbulent combustion however, thin flame-like structures arise in the solution of the Stochastic Fields equations that require grid spacing much finer than the filter scale used for the Large Eddy Simulation. The conventional approach of using grid spacing equal to the filter scale yields substantial numerical error, whereas using grid spacing much finer than the filter length scale is computationally-unaffordable for most industrially-relevant combustion systems. A Thickened Stochastic Fields approach is developed in this study in order to provide physically-accurate and numerically-converged solutions of the Stochastic Fields equations with reduced compute time. The Thickened Stochastic Fields formulation bridges between the conventional Stochastic Fields and conventional Thickened-Flame approaches depending on the numerical grid spacing utilised. One-dimensional Stochastic Fields simulations of freely-propagating turbulent premixed flames are used in order to obtain criteria for the thickening factor required, as a function of relevant physical and numerical parameters, and to obtain a model for an efficiency function that accounts for the loss of resolved flame surface area caused by applying the thickening transformation to the Stochastic Fields equations. The Thickened Stochastic Fields formulation is tested by performing LES of a laboratory premixed Bunsen flame. The results demonstrate that the Thickened Stochastic Fields method produces accurate predictions even when using a grid spacing equal to the filter scale. The present development therefore facilitates the accurate application of the Stochastic Fields approach to industrially-relevant combustion systems.

中文翻译：

---

湍流燃烧模拟的加厚随机场方法

随机场方法是将传输概率密度函数建模应用于湍流燃烧大涡模拟的有效方法。然而，在预混湍流燃烧中，在随机场方程的求解中会出现薄的火焰状结构，该方程要求的网格间距比用于大涡模拟的过滤器尺寸要细得多。使用等于过滤器尺度的网格间距的传统方法会产生很大的数值误差，而使用比过滤器长度尺度更精细的网格间距对于大多数工业相关燃烧系统来说在计算上是无法承受的。本研究开发了一种加厚随机场方法，以便在减少计算时间的情况下提供随机场方程的物理精确且数值收敛的解。加厚随机场公式根据所使用的数值网格间距，在传统随机场和传统加厚火焰方法之间建立了桥梁。使用自由传播的湍流预混火焰的一维随机场模拟，以获得所需增稠因子的标准，作为相关物理和数值参数的函数，并获得考虑损失的效率函数模型通过将增厚变换应用于随机场方程而引起的解析火焰表面积。通过对实验室预混合本生火焰进行 LES 测试，对加厚随机场配方进行了测试。结果表明，即使使用等于滤波器比例的网格间距，加厚随机场方法也能产生准确的预测。因此，目前的发展促进了随机场方法在工业相关燃烧系统中的准确应用。