高浓度固-液两相流紊流的动理学模型

采用分子动理学方法,基于固-液两相流液相分子或颗粒相颗粒的Boltzmann方程,对Boltzmann方程分别取零矩和一次矩,则得到高浓度固-液两相流紊流的连续方程和动量方程,再和较成熟的低浓度两相流连续方程和动量方程比较,取低浓度两相流控制方程中较成熟合理的有关项和高浓度时由动理学方法推导出的颗粒间碰撞项,则得到高浓度固-液两相流紊流的最终控制方程:连续方程和动量方程.

KINETIC MODEL FOR SILT-LADEN SOLID-LIQUID TWO-PHASE FLOW

So far, most research scholars have widely investigated the dilute solid-liquid flow from macro-continuum theory, and firstly on the assumption that the motions of particles are motivated by ambient liquid and have no any relations with the collisions between particles, and then based on Reynold-averaged equations, thus two-phase flow governing equations are well established by a series of averaging means in terms of continuum theory and a lot of good results are obtained. But under the dense solid conditions, dense two-phase flow is quite different from dilute one. Except that the particles of dense flow have the same flow properties as the particles of the dilute flow, these collisions between particles are not neglected; thereby viscosity and diffusion from particlecollisions should be considered. At the same time, it is difficult to gain the collisions pressure be-tween particles from the macro-continuum theory. But based on Boltzmann equation, the kinetic theory can well describe microscopic interaction properties and nowadays, there are three investi-gating means on solid-liquid two-phase flow: (1) Boltzmann equation velocity distribution function method; (2) Boltzmann equation integrating method; (3) LBM (Lattice Boltzmann Method). In the paper, gas molecular kinetic theory is applied to dense solid-liquid two-phase flow from their microcosmic flow characters. Multiplying every phase Boltzmann equation by their characteristic parameters and integrating over the velocity space, the continuum and moment equations for the solid-phase two-phase flow are obtained from molecular or particle microcosm. The governing equations for dense two-phase flow are compared with the dilute well-developed solid-liquid ones, then both considering that the collisions between particles are not neglected under the particular conditions for the dense two-phase flow and assumed that every phase velocity distribution obeys the Maxwell equations, the collisions between particles is also obtained from microcosm. Finally by adopting the reasonable items from the dilute two-phase governing equations and the collision items, the governing equations are derived for dense slid-laden turbulent flow. Prom the viewpoint of microscope of -phase molecule or particle, every term in equation shows clear definition.