非均匀悬移质泥沙弥散速度本构方程

天然河流中泥沙由非均匀颗粒组成,泥沙的非均匀性对于水沙运动和河床演变过程具有重要影响。然而目前非均匀悬移质泥沙研究中很少考虑不同粒径颗粒相互作用,颗粒相互作用对非均匀沙悬浮的贡献仍不明确。本文旨在建立非均匀悬移质泥沙弥散速度本构方程,其可反映非均匀泥沙悬浮的主要力学机制。首先,基于固液两相流理论,建立非均匀沙挟沙水流的两相流方程,充分考虑不同粒径颗粒相互作用力,并推导挟沙水流两相浑水方程以避免相间作用耦合复杂的问题。其次,为封闭两相浑水方程,引入弥散速度的概念,建立非均匀沙各粒径组弥散速度本构方程,揭示非均匀沙悬浮本质上是浑水紊动、颗粒自身作用、其他粒径颗粒作用三种作用共同影响的结果。最后,基于非均匀沙弥散速度本构方程得到非均匀悬移质泥沙的输沙方程,分析非均匀沙浓度垂线分布规律,将其应用于明渠恒定均匀流中,计算的非均匀沙浓度垂线分布与实验数据能较好地吻合。相对于均匀沙公式,在浓度相对较高、粒径差异大的条件下,非均匀沙公式的计算值与实验值符合得更好,进一步验证了非均匀沙弥散速度本构方程能够从力学本质上反映不同粒径颗粒相互作用对颗粒悬浮的影响机制。

Drift velocity of non-uniform suspended sediment

In natural rivers, suspended sediment is generally non-uniform in grain sizes, and the non-uniformity is a major factor in sediment transport and fluvial processes. However, previous studies on non-uniform sediment transport lack attention on the interactions between different grain sizes, and the non-uniformity effect on sediment suspension remains unclear. To elucidate this effect, this paper presents a constitutive equation for the drift velocity of non-uniform suspended sediment. First, applying the two-phase flow theory, we develop basic governing equations of flows and non-uniform sediment transport, focusing on the particle-particle interactions between sediment groups of different grain sizes, and derive two-phase mixture equations for non-uniform sediment-laden flows that can be used to save complicated calculation of interphase interactions. Then, drift velocity is introduced for closure of the two-phase mixture equations, and its constitutive equation is developed to describe the fact that the suspension of non-uniform sediment is attributed to influences imposed by flow turbulence, sediment particles themselves, and more importantly, interaction between particles in different grain sizes. This fact distinguishes the non-uniform sediment transport from the uniform one. Finally, we construct transport equations for non-uniform sediment using this constitutive equation, and obtain vertical concentration profiles for each grain size of the mixture. Comparison of these profiles with measurements shows a good agreement, and we demonstrate the difference from the uniform sediment cases through comparing the profiles to those calculated using Rouse formula. Result shows that when the concentration is higher and the disparity in grain sizes wider, the difference in the vertical profiles between the uniform and non-uniform methods becomes more distinct, and particle-particle interactions play a more important part in sediment suspension. The constitutive equation of drift velocity provides a theoretical way to elucidate the essence and effect of particle-particle interactions on suspension of non-uniform sediment.