Turbulence–chemistry interaction models such as the conditional moment closure and various flamelet models require a presumed Probability Density Function (PDF) model of the conditioning variables. In turbulent stratified flames, a joint-PDF model for a reaction progress variable and the mixture fraction is required. The joint-PDF is often modelled by two beta functions using the first and second moments of the two conditioning variables. In this work, the performance of a joint-PDF model based on the flamelet PDF approach is compared to the double beta-PDF model. The conditional PDF of the reaction progress variable conditioned on mixture fraction is modelled with the flamelet PDF. Unlike the beta PDF, the flamelet functional form for the conditional PDF varies with the local mixture fraction. The two PDF models are coupled with a two-dimensional premixed flamelet-generated manifold chemistry model. Two stratified flames of the Cambridge–Sandia bluff-body burner are simulated using a Reynolds-Averaged Navier–Stokes (RANS) approach. The results indicate that the flamelet PDF model has a superior, albeit marginal, predictions of the temperature, major and minor species mass fractions.

湍流-化学相互作用模型，例如条件矩闭合和各种小火焰模型，都需要假定的条件变量的概率密度函数（PDF）模型。在湍流分层火焰中，需要用于反应进度变量和混合物分数的联合PDF模型。联合PDF通常使用两个条件变量的第一和第二时刻由两个beta函数建模。在这项工作中，将基于Flamelet PDF方法的联合PDF模型与双beta-PDF模型的性能进行了比较。使用小火焰PDF对以混合物分数为条件的反应进程变量的条件PDF进行建模。与beta PDF不同，条件PDF的小火焰函数形式随局部混合物分数而变化。这两个PDF模型与二维预混火焰小波生成的歧管化学模型耦合。使用雷诺平均纳维-斯托克斯（RANS）方法模拟了Cambridge-Sandia钝体燃烧器的两个分层火焰。结果表明，小火焰PDF模型对温度，主要物种和次要物种的质量分数具有较好的预测效果，尽管只有少量预测。