水沙动力学适用牛顿流体的基本方程

通过改进蔡树棠两相流基本方程的相间阻力项,建立能够进行二维解析研究的水沙动力学基本方程.该研究给出沙相压力和沙相粘性切应力的学科定义,以及它们的本构关系.对于牛顿流体,当输沙稳定时,挟沙水流的能坡与清水并无差别.沙相压力的二阶导数不为零是泥沙扩散条件,也是凹岸冲、凸岸淤自然现象的力学本质.蔡树棠方程隐含着流体的粘性切应力按运动组成可以分解或叠加的物理性质.正是这个结构性特点,给了解答浑水粘性这个古老的力学难题的方法,使我们能够完整地推导出牛顿流体沙相运动学粘滞系数vs公式；推导并证明了浑水综合粘滞系数μm=εv+ svνs,而不是习惯使用的μm=v+svvs.探讨了影响vs值的一些复杂因素,如颗粒表面束缚水的影响.本文研究能够证明:对分散相应用连续介质原理不仅可行,且是遵从压力传递规律惟一的正确方法.而揭示粘性切应力的结构性,在多相流和流变学领域具有深远的意义.

Basic equations of water-sediment mixture dynamics for Newtonian fluids

By improving the inter-phase resistance term in Cai Shutang two-phase turbulent flow equations,the basic equations of water-sediment dynamics for Newtonian fluids that are able to conduct two dimensional analytical study have been established.This study gives the discipline definition of sediment phase pressure and sediment phase viscous shear stress,and their constitutive relations.For a Newtonian fluid,when the transported sediment is stable,the energy slope of silt-carrying flow is no difference with that of clear water.The second derivative of sediment phase pressure not to be zero is a condition of sediment diffusion,and is the mechanics nature of natural phenomenon of erosion at concave banks and silting at convex banks.Cai Shutang equation implies a physical property of fluid viscous shear stress that can be resolved or superposed by movements composed.It is this structural feature gives a solution to the old mechanics problem of muddy water viscosity,and allows us to derive full sediment phase kinematic viscosity coefficient formula;and to derive and prove the synthetic viscosity of muddy water to be μm=εν+sVνs,rather than the use of μm=ν+sVνs.Complex factors affecting the νs value,such as the attached water on the particle surface and Bingham shear stress for very fine particles are discussed.Study of two dimensional analysis can prove that applying the continuum principle to diffuse phase not only is viable,but also is the right way to comply with the pressure transmission.And revealing the viscous shear stress of structural nature has a far-reaching significance in the field of multiphase flow and rheology.