考虑剪切扩散系数的垂线含沙量分布：基于同伦分析方法的显式级数解
Vertical sediment concentration distribution revisited with shear-induced diffusivity: An explicit series solution based on homotopy analysis method
摘要：
本文重新研究了明渠水流中悬浮泥沙浓度的垂向分布，并特别考虑了泥沙扩散系数。如果湍流扩散率被认为遵循抛物线型剖面，则扩散系数在床面处为零，而在床面附近非常小;因此，仅凭它可能不足以将颗粒从推移质层扩散到悬浮区。Leighton & Acrivos（J. Fluid Mech.，第181卷，1987年，第181页。415-439）引入了由于固体颗粒之间的流体动力学相互作用而产生的剪切诱导扩散的想法。这项工作认为亨特扩散方程纳入剪切诱导扩散的概念，并重新调查的垂直含沙量剖面。解析解推导使用非微扰的方法，即同伦分析方法（HAM），并验证了数值解，以及与现有的实验数据进行比较。从物理上解释了剪切扩散系数随垂直距离和颗粒直径的变化规律。此外，重要的湍流因素，如施密特数的倒数，受阻沉降速度对浓度分布的影响，已考虑相关的实验数据集进行了研究。
英文摘要：
The present study revisits the vertical distribution of suspended sediment concentration in an open channel flow with a special attention to sediment diffusion coefficient. If turbulent diffusivity is considered to follow a parabolic-type profile, the diffusivity coefficient is zero at the bed and very small near the bed; so alone it may not be enough to diffuse the particles from bed-load layer to suspension region. Leighton & Acrivos (J. Fluid Mech., vol. 181, 1987, pp. 415-439) introduced the idea of shear-induced diffusion that arises due to the hydrodynamic interactions between solid particles. This work considers the Hunt diffusion equation incorporating the concept of shear-induced diffusion and reinvestigates the vertical sediment concentration profile. Analytical solution is derived using a non-perturbation approach, namely Homotopy Analysis Method (HAM), and is verified with numerical solution as well as compared with available experimental data. The behaviour of the shear-induced diffusion coefficient with vertical distance and varying particle diameters have been interpreted physically. In addition, the effects of important turbulent factors such as inverse of Schmidt number, hindered settling velocity on concentration profile, have been investigated considering relevant sets of experimental data.
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