The inclusion of molecular diffusion into the joint-probability density function (JPDF) method requires terms for molecular transport in physical space and mixing in composition space. The former is typically neglected for high Reynolds number flows but becomes important in flows close to surfaces and for flamelet related reaction-diffusion structures associated with high Damköhler numbers. McDermott and Pope (J. Comp. Phys., 2007) proposed an explicit addition of a molecular transport term to the equation for sub-grid molecular diffusion for the filtered density function method. A related approach was used by Fiolitakis et al. (Combust. Flame, 2014) for the JPDF method when combined with moment based closures. A variant of the method is here combined with comprehensive ${\mathrm{C}}_1-{\mathrm{C}}_2$ chemistry featuring 44 chemical species and 256 reactions to study the impact on auto-ignition and flame stabilisation in the well-characterised Cabra burner. It is shown that the contribution of the molecular transport term becomes significant at the flame stabilisation point with predictions of carbon monoxide and, in particular, molecular hydrogen showing a marked improvement. Conditional statistics and the PDF of temperature show that the improvement is due to increased molecular diffusion on the fuel rich side of the flame leading to increased chemical activity. The developed approach is viable for boundary layers while the spatial resolution requirements in terms of the mean scalar gradients may prove limiting for complex flows.

将分子扩散纳入联合概率密度函数 (JPDF) 方法需要物理空间中的分子传输和组合空间中的混合项。对于高雷诺数流动，前者通常被忽略，但在靠近表面的流动和与高 Damköhler 数相关的小火焰相关反应扩散结构中变得重要。McDermott 和 Pope (J. Comp. Phys., 2007) 建议在过滤密度函数方法的子网格分子扩散方程中明确添加分子传输项。Fiolitakis 等人使用了一种相关的方法。(Combust. Flame, 2014) 与基于矩的闭包相结合时的 JPDF 方法。该方法的一个变体在这里结合了全面的${\mathrm{C}}_1-{\mathrm{C}}_2$化学具有 44 种化学物质和 256 种反应，用于研究对特性良好的 Cabra 燃烧器中自燃和火焰稳定性的影响。结果表明，分子传输项的贡献在火焰稳定点变得显着，预测一氧化碳，特别是分子氢显示出显着改善。条件统计和温度的 PDF 表明，改进是由于火焰富燃料侧的分子扩散增加导致化学活性增加。开发的方法对于边界层是可行的，而平均标量梯度方面的空间分辨率要求可能会限制复杂流。