将基于Langevin方程的多分散两相流PDF模型应用于钝体气固两相流，
PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,
摘要：
本文的目的是讨论一个完整的多分散两相湍流理论和数值模型的主要特点，指出一些具体问题。该模型的理论细节已经介绍过[Minier和Peirano，Physics Reports，Vol.352/1-3，2001 ]。因此，目前的工作主要侧重于补充方面，这些方面往往被忽视，但需要特别注意。特别是，以下几点进行了分析：在双向耦合的情况下看到的流体的速度的方程中添加一个额外的项的必要性，颗粒平均值的理论和数值评价和颗粒质量连续性约束的履行。理论模型是在PDF形式主义。首先讨论了状态向量变量的重要物理选择，然后将模型表示为连续时间（Langevin方程）中所见流体速度的随机微分方程（RSDs）。与单相情况相比，朗之万方程的利益和局限性进行了审查。从数值的角度来看，该模型对应于混合欧拉/拉格朗日方法，其中流体和颗粒相通过不同的方法进行模拟。Monte Carlo粒子/网格数值方法的重要方面进行了强调。最后，完整的模型进行了验证，并通过模拟一个重要的回流区和双向耦合是显着的钝体情况下，其性能进行评估。
英文摘要：
The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasised. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.
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