Robust interpolation for dispersed gas-droplet flows using statistical learning with the fully Lagrangian approach,International Journal for Numerical Methods in Fluids

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Robust interpolation for dispersed gas-droplet flows using statistical learning with the fully Lagrangian approach
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2023-07-05 , DOI: 10.1002/fld.5225
C. P. Stafford ₁ , O. Rybdylova ₁

Affiliation

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

1 0^{3} $$ 1{0}^3 $$

times fewer droplet realisations are needed to reconstruct a qualitatively similar representation of the number density field.

中文翻译：

使用完全拉格朗日方法的统计学习对分散气体液滴流进行鲁棒插值

提出了一种新颖的方法，用于重建使用完全拉格朗日方法（FLA）建模的分散气体液滴流的欧拉数密度场。在这项工作中，核回归的非参数框架用于根据分散相的空间结构累积单个液滴的 FLA 数密度贡献。通过使用作为 FLA 核心的欧拉-拉格朗日变换张量来解释在非定常流的液滴数密度场中观察到的高度变化，以指定与每个液滴相关的核的大小和形状。该过程能够保留高水平的结构细节，并且事实证明，为了重建分散相的忠实欧拉表示，需要跟踪的液滴要少得多。此外，核回归过程很容易扩展到更高的维度，并且使用广义完全拉格朗日方法（gFLA）将液滴半径包含在相空间描述中还可以确定多分散流的液滴尺寸分布的统计数据。所开发的方法适用于单分散和多分散液滴的一系列一维和二维稳态和瞬态流，并且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，以确定可以节省的计算费用，结果发现：