This paper provides an improved flamelet/progress variable (FPV) model forthe simulation of turbulent combustion, employing the statistically most likelydistribution (SMLD) approach for the joint probability density function (PDF)of the mixture fraction, Z, and of the progress parameter, {\Lambda} .Steady-state FPV models are built presuming the func- tional shape of the jointPDF of Z and {\Lambda} in order to evaluate Favre-averages of thermody- namicquantities. The mixture fraction is widely assumed to behave as a passivescalar with a mono-modal behaviour modelled by a \b{eta} -distribution.Moreover, under the hypothesis that Z and {\Lambda} are statisticallyindependent, the joint PDF coincides with the product of the two marginal PDFs.In this work we discuss these two constitutive hypotheses. The proposed modelevaluates the most probable joint distribution of Z and {\Lambda} , relaxingsome crucial as- sumption on their statistical behaviour. This provides a moregeneral model in the context of FPV approach and an effective tool to verifythe adequateness of widely used hypotheses. The model is validated versusexperimental data of well-known test cases, namely, the San- dia flames. Theresults are also compared with those obtained by the standard FPV approach,analysing the role of the PDF functional form on turbulent combustionsimulations.
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机译：本文为湍流燃烧的模拟提供了一种改进的小火焰/进度变量（FPV）模型，该方法对混合分数Z和进度参数的联合概率密度函数（PDF）采用了统计上最可能分布（SMLD）方法， {\ Lambda}。假定Z和{\ Lambda}的联合PDF的函数形状为函数，则建立稳态FPV模型，以评估热力学量的Favre平均。广泛假设混合分数具有通过\ b {eta}分布建模的单峰行为的被动标量。此外，在Z和{\ Lambda}在统计上独立的假设下，联合PDF与乘积一致两个边际PDF中的一个。在这项工作中，我们讨论了这两个本构假设。提议的模型评估Z和{\ Lambda}的最可能的联合分布，放松了对其统计行为的一些关键假设。这在FPV方法的背景下提供了更通用的模型，并且是验证广泛使用的假设是否适当的有效工具。该模型已针对著名测试案例（Sandia火焰）的实验数据进行了验证。将结果与通过标准FPV方法获得的结果进行了比较，分析了PDF函数形式在湍流燃烧模拟中的作用。
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