Robust interpolation for dispersed gas‐droplet flows using statistical learning with the fully Lagrangian approach
Robust interpolation for dispersed gas‐droplet flows using statistical learning with the fully Lagrangian approach
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DOI：
10.1002/fld.5225
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发表时间：
2022-04
影响因子：
1.8
通讯作者：
C. Stafford;O. Rybdylova
中科院分区：
文献类型：
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作者：
C. Stafford;O. Rybdylova
提出了一种新的方法来重建离散气滴流的欧拉数密度场，该方法使用完全拉格朗日方法（弗拉）建模。在这项工作中，核回归的非参数框架被用来积累的弗拉数密度的贡献，根据分散相的空间结构的个别液滴。通过使用欧拉-拉格朗日变换张量（弗拉的中心）来说明在非定常流的液滴数密度场中观察到的高变化，以指定与每个液滴相关的核的大小和形状。该过程能够保持高水平的结构细节，并且证明了为了重建分散相的忠实欧拉表示，必须跟踪少得多的液滴。此外，内核回归程序很容易扩展到更高的维度，并列入液滴半径内的相空间描述使用的广义完全拉格朗日方法（gFLA），另外使统计的液滴尺寸分布要确定多分散流。所开发的方法适用于一系列一维和二维稳态和瞬态流，单分散和多分散液滴，它表明，核回归在这种情况下表现良好。与传统的直接轨迹方法进行比较，以确定可以获得的计算费用的节省，并且发现需要少103 $$1 {0}^3 $$倍的液滴实现来重建数量密度场的定性相似表示。
A novel methodology is presented for reconstructing the Eulerian number density field of dispersed gas‐droplet flows modelled using the fully Lagrangian approach (FLA). In this work, the nonparametric framework of kernel regression is used to accumulate the FLA number density contributions of individual droplets in accordance with the spatial structure of the dispersed phase. The high variation which is observed in the droplet number density field for unsteady flows is accounted for by using the Eulerian‐Lagrangian transformation tensor, which is central to the FLA, to specify the size and shape of the kernel associated with each droplet. This procedure enables a high level of structural detail to be retained, and it is demonstrated that far fewer droplets have to be tracked in order to reconstruct a faithful Eulerian representation of the dispersed phase. Furthermore, the kernel regression procedure is easily extended to higher dimensions, and inclusion of the droplet radius within the phase space description using the generalised fully Lagrangian approach (gFLA) additionally enables statistics of the droplet size distribution to be determined for polydisperse flows. The developed methodology is applied to a range of one‐dimensional and two‐dimensional steady‐state and transient flows, for both monodisperse and polydisperse droplets, and it is shown that kernel regression performs well across this variety of cases. A comparison is made against conventional direct trajectory methods to determine the saving in computational expense which can be gained, and it is found that 103$$ 1{0}^3 $$ times fewer droplet realisations are needed to reconstruct a qualitatively similar representation of the number density field.