风沙两相流跃移层中沙粒相的速度分布

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Boltzmann方程，对风沙流研究中几种不同的分布函数及其相应的统计平均值等基本概念给出了严密的数学定义，指出了不同分布函数之间的区别和联系，在略去铅垂方向空气阻力的情况下，给出了沙粒相速度分布函数沿铅垂方向的边缘分布，作为风沙流中跃移理论的主要基础之一。利用结果对前人在风沙流研究中发现的某些重要规律和现象进行了解释。

VELOCITY DISTRIBUTION OF PARTICLE PHASE IN SALTATING LAYER OF WIND-BLOWN-SAND TWO PHASE FLOWS

In this paper, Boltzmann equation for velocity distribution function of the particle phase in wind-blown sand two phase flow is derived from the motion equation of single particle saltating in the air flow. Exact mathematical definitions are given for several different distribution function, which are usually confused in literature, such as velocity distribution function in 3-D space, velocity distribution function of particle launching across plane, saltation height distribution function. The difference and relationship among them are pointed out. Several macroscopic average quantities corresponding to each distribution function are introduced. The particle flux in unit wide is expressed in terms of these introduced statistical mean quantities. Some important phenomena found previously in airborne movement are properly explained by the theory developed in this paper. In the case of ignoring vertical drag in boundary layer, it is approved that the following 5 propositions airs equivalent to each other: (1) The velocity distribution function of particle launching across horizontal plane is Rayleigh distribution. (2) The boundary distribution along y direction of velocity distribution function in 3-D space is normal distribution. (3) Saltation height distribution function across horizontal plane is normal distribution. (4) the particle mass density attenuates as an exponential function of height y. (5) The second order moment of velocity distribution along y direction is constant. The stroboscopic photography method in the wind tunnel test is used to measure the particle speeds, and particle flux is test by sand-collection. The present experimellts and previous literature show that the above 5 propositions are good approximations to approach experiments.