重力沉降颗粒的湍流相对扩散、焦散及聚集效应

Preferential concentration and caustics are the two most important characheristics of heavy particles driven by turbulence, where the preferential concentration means particles do not uniformly distribute in the turbulent flow field,but preferentially accumulate in regions of low vorticity and high strain rate due to the centrifugal force of the turbulent eddies, and the caustics means multiple values of particle velocity at the same point in the turbulent flow field due to the sling effect of eddies with high local dissipation rate, known as intermittence of turbulence. Preferential concentration and caustics significantly affect the collision rate between heavy particles and thus the physical and chemical reaction rates. The relative dispersion of heavy particles by turbulence results in these two important characteristics. The isotropic turbulence field is solved using the pseudo spectral method, and Lagrangian tracking is used to solve the motion of particles based on the point-particle assumption. The four-way coupling method between particle and turbulence, particle and particle collision is considered. Gravity makes the interaction time between particles and the isotropic turbulence anisotropic. The main contents of the projection include(1)the effects of Stokes number, Reynolds number and Froude number on preferential concentration, relative velocity and caustics;(2) the effects of Stokes number, Reynolds number and Froude number on the time asymmetry of forward-in-time and backward-in-time relative dispersions;(3) the construction of the anisotropic diffusivity tensors in the kinetic equation for two-particle PDF of the particle pair relative velocity distribution;(3) the coupling between the approximate deconvolution method and stochastic differential equation to recover the subgrid scale turbulent velocity seen by heavy particles. The results of this project are of significance to give physical insight to the mechanism of relative dispersion, preferential concentration and caustics under gravity, and will help to improve the accuracy of large-eddy simulation of relative dispersion of heavy particles.

重颗粒在湍流涡离心力和重力作用下，可表现出聚团和焦散效应（流场中同一点对应多个不同的颗粒速度）等显著特征，从而影响颗粒碰撞率及物理或化学反应速率。它们是颗粒对在湍流作用下相对扩散的结果。我们采用直接数值模拟的方法求解各向同性湍流场，采用拉格朗日方法跟踪颗粒，其中颗粒采用点力模型，同时考虑颗粒与湍流、颗粒与颗粒间4向耦合作用。重力的引入使得颗粒与各向同性湍流的作用时间变得各向异性。主要研究内容包括：不同湍流雷诺数、颗粒Stokes数及重力Froude 数下(1)颗粒聚团、颗粒相对速度和焦散效应;(2)颗粒的时间正向、反向相对扩散时间的非对称性；（3）相对速度概率密度函数动理学方程中各向异性扩散系数的构建；（4）反卷积与随机微分方程耦合的颗粒亚格子模型等。课题预期结果对加深理解沉降速度、颗粒惯性对湍流相对扩散、颗粒聚集和焦散效应及提高大涡模拟预测相对扩散的精度等方面有重要的科学意义。

携带颗粒的湍流在人们日常生活、环境和工业流动中广泛存在，例如河流中泥沙的输运，大气中污染物的扩散，大气中雨滴的形成，发动机喷雾燃烧等。研究湍流中的重颗粒在湍流涡结构离心力和重力双重作用下的聚团、相对运动以及焦散效应（流场中同一点具有多个不同的颗粒速度）机理具有重要的科学意义和应用价值。我们采用直接数值模拟的方法求解各向同性湍流场，采用拉格朗日方法跟踪颗粒，其中颗粒采用点力模型。主要研究内容包括不同湍流雷诺数、颗粒Stokes数及重力Froude 数下颗粒聚团、颗粒相对速度和焦散效应的物理机制；颗粒的正向、反向相对扩散时间的非对称性；反卷积与运动学合成湍流的颗粒亚格子模型等。通过该项目，我们提出了沉降颗粒对在湍流中沉降特征时间尺度模型，并利用该时间尺度提出了一个依赖于沉降速度的等效Kubo 数的概念。在大Stokes 数，小Kubo数下，湍流中在重力作用下增强颗粒聚团程度的机理是颗粒在无关联的随机场中运动过程中，在颗粒惯性和乘积放大机理作用下，颗粒的聚集增强。我们基于时间向后扩散，研究了颗粒相对速度概率密度分布函数的变化趋势。在大Stokes 下颗粒相对速度间歇性增强归因于颗粒无法有效分离，颗粒对倾向于遍历间歇性更强的小尺度湍流结构，最终导致颗粒的相对速度的间歇性增强。在小Stokes 数下，颗粒的聚集程度变弱，颗粒分布更加均匀，颗粒对遍历流场速度梯度也更加均匀，使得颗粒相对速度的间歇性变弱。