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Lagrangian filtered density function for LES-based stochastic modelling of turbulent particle-laden flows

机译:拉格朗日滤波密度函数用于基于LES的湍流含颗粒流的随机建模

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摘要

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture the particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.
机译:当直接数值模拟(DNS)的计算成本变得过高时,基于大涡模拟(LES)的欧拉-拉格朗日方法是研究充满粒子的湍流的最有前途和可行的数值工具之一。但是,如果忽略了流的子网格比例(SGS)对粒子动力学的影响,则该方法的适用性受到限制。在本文中,我们建议通过拉格朗日随机SGS模型将这些影响考虑在内。该模型扩展到载有颗粒的流,该流过滤的密度函数方法最初是为反应流开发的。通过Lagrangian蒙特卡洛程序模拟了基本的滤波密度函数,该函数求解了沿各个粒子轨迹的一组随机微分方程(SDE)。使用混合算法对生成的模型进行湍流通道参考情况的测试,在该算法中,LES提供了流体速度场,然后用于及时推进SDE。当可从欧拉LES和拉格朗日跟踪中获得“重复场”时,在零惯性粒子的极限中评估模型的一致性。进行了惯性粒子测试,以检验模型捕获粒子优先浓度和近壁偏析的能力。与基于DNS的统计数据进行比较后,相对于在粒子运动方程中不使用SGS模型的情况,我们的结果显示出更高的准确性,并大大减少了误差。

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