Abstract: With Langevin equation of particle motion,PDF equations in two levels are obtained in which the fluid fluctuation velocity is expanded in dimension and one-dimensional colored noise is transformed into two-dimensional white noise.They are two-phase PDF transport equation of turbulence and particle-phase PDF transport equation.With particle motion equations and assumption of Gaussian distribution,a closure problem of PDF equation is solved and a second-order-moment model is obtained.It is simplified into an algebra stress model [ASM].A finite analytic numerical method for convective diffusion equation is applied to solve the two-order moment model of two-phase flows.A wall-jet-flow loaded with solid particles is studied in the ASM by finite analytic numerical method.Numerical results are compared with experimental results.

Key words: turbulence, method of expanded dimension, two-phase flow, numerical simulation, colored noise, second order moment model