Abstract

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, “folds” and “puckers” of the phase volume may arise, and “caustics” (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows.

This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of “gas-particle” media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media.

中文翻译：

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用于模拟稀分散介质流的完整拉格朗日方法的发展（综述）

摘要

零压力介质的连续体模型广泛应用于物理和力学的各个分支，包括多相流中稀分散相的研究。在零压力介质中，粒子轨迹可能相交，可能出现相体积的“折叠”和“褶皱”，并且可能出现“焦散”（粒子轨迹的包络线），在其附近介质的密度急剧增加。近几十年来，气液流中惯性混合物的团聚和气动聚焦现象越来越受到研究者的关注。这是因为在描述环境中气溶胶污染物的传输、雨云中液滴生长的机制、分散夹杂物的辐射散射、两相中爆炸的引发时，必须考虑杂质浓度的不均匀性。混合物，以及解决两相空气动力学问题、解释通过 LDV 或 PIV 方法获得的测量结果以及许多其他应用。这些问题推动了致力于气体和液体流中惯性粒子的积累和聚集过程的出版物数量的显着增加。在假设介质连续介质参数单值的经典双流体模型和标准欧拉方法的框架内，事实证明不可能描述具有交叉粒子轨迹的流中的多值速度场和密度奇点区域。其中一种替代方案是作者之前提出的完整拉格朗日方法。近年来，这种方法结合平均欧拉法和拉格朗日法（涡斑法）得到了进一步发展，用于描述载波相位的动力学。这种组合方法使得研究涡流、瞬态流和湍流中惯性粒子积累的局部区域的结构成为可能。

本文描述了完整拉格朗日方法的基本思想，提供了最重要结果的示例，说明了该方法的独特功能，并概述了该方法进一步发展的主要方向，适用于瞬态、涡流和“气体-粒子”介质的湍流。下面讨论的一些想法和下面提出的结果具有更普遍的意义，因为它们也适用于其他零压力介质模型。