低浓度固液两相流的颗粒相动理学模型  

KINETIC MODEL OF PARTICULATE PHASE IN DILUTE SOLID-LIQUID TWO-PHASE FLOWS

作　　者：傅旭东[1] 王光谦[1] 

机构地区：[1]清华大学水利系水沙科学教育部重点实验室,北京100084

出　　处：《力学学报》2003年第6期650-659,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金和水利部联合资助重大项目(59890200);清华大学骨干人才支持计划;清华大学水利系基础研究基金资助

摘　　要：用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用,用修正的BGK模型描述粒间碰撞效应,建立了封闭的颗粒相PDF输运方程.运用Chapman-Enskog迭代法求得方程的二阶近似解,获得颗粒相脉动速度二阶矩和三阶矩闭合关系.模型与颗粒流模型相容,与液相湍流闭合模型是否相容依赖于扩散模型的具体形式,并据此比较了不同的涡-颗粒作用模型.模型与二维明渠流轻质沙和天然沙试验资料符合很好.表明细小粒径颗粒能够充分跟随水流运动;大粒径颗粒的相间平均速度差和壁面滑移速度明显,近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流,并存在一定程度的颗粒碰撞效应.A closed PDF equation for particles was developed by using a generalized Fokker-Planck diffusion model for particle entrainment into liquid turbulence eddies and a modified BGK model for particle collisions. Chapman-Enskog iteration method was employed to find the second-order approximation solution to the PDF equation. The closure relations of the second and third moments of particle velocity fluctuations, which are consistent with the granular theory based on Boltzmann equation, were further derived. Whether the closure consists with that of liquid turbulence as Stokes number St→0 depends on the special diffusion model, and several particle-eddy interaction models were compared. The kinetic model agrees well with experimental data of polystyrene particles and that of natural sands in two-dimensional open-channel flows. It is shown that fine particles follow water turbulence very well, while large particles have distinct velocity difference with water and slip velocity at the wall. In the near wall region, the longitudinal and vertical velocity fluctuations of large particles may exceed those of water, and particle collisions may also be significant for flows with natural sands and high concentration.

关 键 词：三阶矩 输运方程 二阶 近似解 近壁区 脉动速度 颗粒 闭合 试验资料 低浓度 

分 类 号：O359[理学—流体力学] O357[理学—力学]