中文摘要：

统一色噪声近似方法对简单一维色噪声问题研究较为充分，本文将统一色噪声法应用到高度复杂的多维气固两相湍流系统之中。首先从颗粒运动Langevin方程出发，利用统一色噪声法获得两相湍流Fokker-Planck方程，然后以此为基础建立颗粒轨道两阶矩模型。文中建立的新模型成功应用于后台阶两相湍流流场的数值模拟，预报合理正确。研究表明，对于多维两相湍流系统，统一色噪声法仍然行之有效。

英文摘要：

A unified colored-noise approximation （UCNA） method has been widely used to solve the simple one-dimensional problem, and this paper attempts to extend this method to multi-dimensional systems. Firstly, a Fokker-Planck equation is obtained by UCNA method based on the Langevin equation for particle motion, then a two-order moment trajectory model is established on this basis. The new model can be successfully used to predict the backward-facing step two-phase flow, and the simulation results agree well with the measurements. This study shows that the UCNA method is still effective in dealing with multi-dimensional two-phase turbulent systems.