Abstract An equation for the probability density function (PDF) for particle velocity and coordinates in a gas turbulent flow is derived. The system of equations for the first and second moments of particle velocity fluctuations is obtained. Using a method similar to Grad’s method, an approximate solution of the PDF equation was found. Based on this approximate solution, the system of equations for the averaged concentration, velocity, and second moments of particle velocity fluctuations was closed. Also, using an approximate solution, the boundary conditions on the rough wall of the channel were obtained. The boundary conditions self-consistently take into account the direction of the velocity vector of particles colliding with the surface, as well as the direction of the normal to a random plane that simulates the roughness. The fundamental difference between the mechanisms of generation of random motion of particles in channels with smooth and rough walls is shown. Copyright © 2020 American Association for Aerosol Research

中文翻译：

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粗糙壁通道中分散湍流的概率模型

摘要 推导了气体湍流中粒子速度和坐标的概率密度函数(PDF)方程。获得了粒子速度波动的一阶和二阶矩的方程组。使用类似于 Grad 方法的方法，找到了 PDF 方程的近似解。基于这个近似解，粒子速度波动的平均浓度、速度和二阶矩的方程组是闭合的。此外，使用近似解，获得了通道粗糙壁上的边界条件。边界条件自洽地考虑粒子与表面碰撞的速度矢量的方向，以及模拟粗糙度的随机平面的法线方向。显示了在具有光滑壁和粗糙壁的通道中产生粒子随机运动的机制之间的根本区别。版权所有 © 2020 美国气溶胶研究协会