An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

混合分数的概率密度函数 (PDF) 的准确预测对于预测燃烧至关重要，因为混合在湍流非预混和部分预混火焰中起着重要作用。这项工作提供了对用于预测混合分数 PDF 的大涡模拟 (LES)/过滤密度函数 (FDF) 方法的评估。LES/FDF 方法的优点是它提供了包括混合分数在内的标量统计分布的完整预测。PDF 方法的预测准确性尚未得到充分验证。评估混合分数的 PDF 的预测，一个守恒的标量，是一个重要的起点。悉尼/桑迪亚非均匀入口喷射火焰被用作测试案例。快速比较表明，LES/FDF 预测的混合分数的 PDF 形状与通常假定的 Beta-PDF 以及火焰中的实验数据显着偏离。为了检查差异的来源，我们阐明了在预测、测量和假定形状 PDF 之间的比较中使用的不同 PDF 定义。通过澄清所检查的 PDF 之间的差异，从比较中观察到的差异在很大程度上得到了调和。在测量和预测中，已解析的混合分数的 PDF 均接近于 Beta-PDF，而直接从 LES/FDF 粒子推导出的 PDF 与 Beta-PDF 有显着偏差。进行多模态 PDF 分析和伪收敛分析以提供似是而非的证据来支持预测的多模态 PDF 形状。通过合成 PDF 的构造，子滤波器尺度 FDF 也显示为接近 Beta-PDF，当与 LES 结合时，它支持在假定 PDF 方法中使用的常见假定 Beta-PDF 假设。