颗粒的有限尺寸对颗粒在均匀各向同性湍流中扩散的影响

The Size Effect on the Dispersion of a Particle in a Homogeneous Isotropic Turbulence

摘要: 本文指出固体颗粒对流体湍流运动的响应有不同的机理,颗粒受大涡的粘性拖动,但受小涡的随机碰撞.基于这种原理,本文计算了有限尺寸的固体颗粒在均匀各向同性湍流中的扩散.结果显示存在着二种相互抵消的效应:颗粒的惯性使颗粒长期扩散系数上升,而颗粒尺寸使颗粒的长期扩散系数下降.

Abstract: The mechanism of the response motion of a suspended particle to turbulent motion of its surrounding fluid is different according to size of turbulent eddies. The particle is dragged by the viscous force of large eddies, and meanwhile driven randomly by small eddies. Based on this understanding, the dispersion of a particle with finite size in a homogeneous isotropic turbulence is calculated in this study. Results show that there are two competing effects: when enhanced by the inertia of a particle, the long-term particle diffusivity is reduced by the finite size of the particle.

[1]	Tchen,C.M.Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid,Ph.D.Dissertation,University of Delf(1947).
[2]	Csanady,G.T.,Turbulent diffusion of heavy particles in atmosphere.J.A tmos.Sci.20(1963),201-208.
[3]	Reeks,M.W.,On the dispersion of small particles suspended in an isotropic turbulent fluid,J.Fluid Mech.,83,3(1977),529-546.
[4]	Pismen,L.M.and A.Nir,On the motion of suspended particles in stationary homogeneous turbulence,J.Fluid Mech.,84,1(1978),193-206.
[5]	Hinze,J.O.,Turbulence,Second Edition,McGrall-Hill Book Company(1975),460-471.
[6]	Taylor,J.B.and B.McNamara,Plasma diffusion in two dimensions,Physics of Fluids,14(1971),1492.
[7]	Lundgren,T.S.and Y.B.Pointin,Turbulent self-diffusion,Physics of Fluids,19(1976),355-358.
[8]	Corrsin,S.,Atmospheric Diffusion and Air Pollution,edited by F.N.Frenkiel and P.A.Sheppard,Academic,New York(1959),161-184.
[9]	Xie Ding-guo,Turbulent kinetic energy of particle phase in solid-fluid suspension turbulence,Proceedings of the International Symposium on Multiphase Flows,Hangzhou,China(1987),396-401.
[10]	Kraichnan,R.H.Diffusion by a random velocity field,Physics of Fluids,13(1970),22-31.
[11]	Wells,M.R.and D.E.Stock,The effects of crossing trajectories on the dispersion of particles in turbulent flow,J.fluid Mech.,136(1983),31-61.