A Study on the Turbulent Diffusion of Matter and Small Particles by the Random Fourier Modes Method and Stochastic Model

这个项目已经按照最初的研究计划实施了。本文的研究进展和结果总结如下：对象(A)均匀平均速度三维湍流中体周羽流扩散场的模拟(l)首先，我们研究了网格湍流中（无体情况下）形成的点源羽流扩散场。采用随机傅立叶模态法和双粒子随机模型进行了数值模拟。两种模型的仿真结果与实验结果吻合较好。(2)结合随机傅立叶模态方法和快速畸变理论，模拟了物体周围的湍流场。利用该模拟湍流场，研究了垂直进入圆柱的点源羽流的特性。此外，本文还采用能力密度函数（pdf）方法对网格湍流中的反应性混合层进行了模拟。从那时起，将这种pdf方法应用于圆柱体周围的扩散进行了尝试。目的(B)发展快速畸变理论模拟复杂湍流流动的运动学方法及其在扩散场模拟中的应用。主要研究了均匀湍流剪切流和轴对称收缩/膨胀流的快速畸变理论解析解。结果表明，轴对称收缩/膨胀流动存在时间稳定解，而均匀湍流剪切流动存在时间不稳定解。在初步研究计划的基础上，对管内湍流中物质的扩散场进行了研究。在此基础上，利用直接数值模拟（DNS）得到的粒子拉格朗日运动轨迹估计了均匀各向同性湍流中的波动标量统计量。少

This project has been put through according to the initial research plan. The progress and results of the research are summarized in the following,Object (A) Simulation of plume diffusion field around the body in the three dimensional turbulent flow with a uniform mean velocity(l) At first, we investigated the plume diffusion field from a point source developed in the grid-turbulence (in case of no body). The numerical simulations have been made by the random Fourier modes method and a Two-particle stochastic model. The simulation results obtained by both models show good agreements with the experimental results.(2) The turbulent field around the body has been simulated by combining the random Fourier modes method and the rapid distortion theory. By using this simulated turbulent field, the characteristics of a point source plume running perpendicularly into the cylinder have been examined.Furthermore, the reactive mixing layer in the grid-turbulence has been also simulated by the prob … More ability density function (pdf) method. From this time on, an application of this pdf method to the diffusion around the cylinder has been tried.Object (B) Development of kinematic method to simulate the complex turbulent flows by the rapid distortion theory, ant its application to the simulation of diffusion fieldsMainly, the analytical solutions of the rapid distortion theory for the homogeneous turbulent shear flows and axisymmetric contraction/expansion flows have been surveyed. Consequently, it was found that in cases of the axisymmetric contraction/expansion flows there exist the temporally stable solutions, but the solution for the homogeneous turbulent shear flows are temporally unstable.Besides the initial research plan, the diffusion fields of matter in the turbulent pipe flow has been investigated. Further, the fluctuation scalar statistics in the homogeneous isotropic turbulence were estimated from the Lagrangian trajectories of material particles obtained by the direct numerical simulation (DNS). Less