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《Acta Mechanica Sinica》 1991-01

## THE DISTRIBUTION OF SOLID PARTICLES SUSPENDED IN A TURBULENT FLOW: A STOCHASTIC APPROACH

Shao Xuejun Xia Zhenhuan(Department of Hydraulic Engineering, Tsinghua University)
The random motion of solid particles suspended in two-dimentional turbulent flow is considered in this paper. Mean values of partical velocity and displacement in a direction normal to the mean streamlines of the flow are calculated and it is found out that particle velocity vp can be decomposed into a mean velocity (vp) and a velocity fluctuation vp - (vp) where (vp) is equal to the settling velocity of the same particle in tranquil fluid. A Langevin random differential equation for particle displacement Yp is developed, from which a Fokker-Planck equation for the probability function p(y, t) is derived on the basis of the theory of Markovian process. Thus the distribution of p(y, t) is interrelated to the random motion of the particle. The lift effect to which a particle will be subject in the vicinity of the wall is taken into account and a corresponding Fokker-Planck equation is developed. Analytic solution of this equation shows that the probability density p(y, t) describing particle displacement has a maximum value at y = H where the perpendicular component of the resulting lift force precisely balances the particle gravity. Interpretation of experimental observations reported in the literature is given using this theory.
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