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arXiv 1409.0022physics.comp-phphysics.flu-dyn
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连续-离散混合求解器中基于扩散的粗粒化:在CFD-DEM中的应用

Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Applications in CFD-DEM

Rui Sun, Heng Xiao

摘要:

在这项工作中,粗粒化的方法,作者先前提出的一个配套文件的基础上解决扩散方程的CFD-DEM模拟,粗粒化是用来获得固体体积分数,颗粒相速度,和流体-颗粒相互作用力。通过检查守恒要求,确定了CFD-DEM模拟中求解扩散方程的变量。然后,该算法实现到CFD-DEM求解器的基础上OpenFOAM和LAMMPS,前者是一个通用的,三维CFD求解器的基础上非结构化网格。采用CFD-DEM求解器和基于扩散的粗粒化算法对流化床进行了数值模拟。收敛的结果得到连续细化网格,即使是网格的细胞大小相当于或小于粒径。这是所提出的方法优于许多现有的粗粒度方法的关键优势,并且当CFD网格的一部分中需要小单元来解析某些流动特征(例如,壁边界流中的边界层以及射流和尾流中的剪切层)时,这将是特别有价值的。此外,我们证明了所提出的粗粒化过程所产生的开销计算成本是典型的CFD-DEM模拟中的总成本的一小部分,只要每个单元格的粒子数是相当大的,虽然不可否认的粗粒化的计算开销往往超过了CFD求解器。本算法的其他优点包括更鲁棒和物理上真实的结果,灵活性和易于实现在几乎任何CFD求解器,和清晰的物理解释的算法中所需的计算参数。总之,基于扩散的方法是CFD-DEM模拟的理论上优雅和实际可行的选择。

英文摘要:

In this work, a coarse-graining method previously proposed by the authors in a companion paper based on solving diffusion equations is applied to CFD-DEM simulations, where coarse graining is used to obtain solid volume fraction, particle phase velocity, and fluid-particle interaction forces. By examining the conservation requirements, the variables to solve diffusion equations for in CFD-DEM simulations are identified. The algorithm is then implemented into a CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a general-purpose, three-dimensional CFD solver based on unstructured meshes. Numerical simulations are performed for a fluidized bed by using the CFD-DEM solver with the diffusion-based coarse-graining algorithm. Converged results are obtained on successively refined meshes, even for meshes with cell sizes comparable to or smaller than the particle diameter. This is a critical advantage of the proposed method over many existing coarse-graining methods, and would be particularly valuable when small cells are required in part of the CFD mesh to resolve certain flow features such as boundary layers in wall bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that the overhead computational costs incurred by the proposed coarse-graining procedure are a small portion of the total costs in typical CFD-DEM simulations as long as the number of particles per cell is reasonably large, although admittedly the computational overhead of the coarse graining often exceeds that of the CFD solver. Other advantages of the present algorithm include more robust and physically realistic results, flexibility and easy implementation in almost any CFD solvers, and clear physical interpretation of the computational parameter needed in the algorithm. In summary, the diffusion-based method is a theoretically elegant and practically viable option for CFD-DEM simulations.

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