基于动理学理论的床沙冲刷函数

Bed sediment entrainment function based on kinetic theory

针对泥沙研究中床面泥沙冲刷函数以经验公式为主,难以深入分析紊流随机因素作用下床面泥沙运动与冲刷强度的力学联系的问题,本文基于泥沙运动的动理学理论建立了床面泥沙冲刷函数。论文中,在动理学理论框架下将床沙冲刷通量表示为单位面积和单位时间内在紊流升力、拖曳力、重力等作用下离开床面的泥沙质量(体积)的统计系综平均,并采用泥沙运动的动理学方程确定了冲刷函数中床面泥沙运动的速度分布函数这一关键统计力学变量。论文还将得到的冲刷函数与3家80组不同来源的实验数据以及3家冲刷函数进行了对比,并作为冲刷边界条件用于悬移质输沙的计算。结果表明,本文得到的冲刷函数不仅具有更好的理论基础,且冲刷通量计算值与实验值符合良好,相对误差在[-0.5~0.5]之间的数据占所有数据的87.2%,相比其他冲刷函数具有更好的计算精度;作为边界条件计算得到的冲刷过程中悬移质浓度分布也较好地复原了实验过程。本文的研究表明,基于动理学理论的冲刷函数既反映了微观状态下拖曳力、升力等随机性外力对床面颗粒运动的影响,又反映了颗粒运动的统计规律,从而能更准确地从力学本质上反映水流强度及颗粒大小等对冲刷通量的影响规律,体现了动理学理论在分析床面泥沙运动特征的优势。

A large part of previously obtained entrainment functions were derived empirically due to the difficulties in relating microscopic motion of particles to their statistical properties. Presented in this paper is anew entrainment function derived on the basis of Kinetic Theory for sediment transport. The entrainmentfunction for bed sediment is defined in terms of Kinetic Theory as a statistical ensemble average of the up-ward boundary flux of bed sediment in per unit area and per unit time picked up from bed into motion bylift,drag due to turbulence,gravity and other stochastic forces. The velocity distribution function involvedin the entrainment function is determined by means of the kinetic equation for sediment-laden flows,aspermits us to consider the variety of forces that affect the motion of bed sediments. The entrainment func-tion is also calibrated,verified and compared with 80 runs of 3 different experiments,and furthermore,itis applied to serve as the boundary condition in modeling suspended sediment distribution in a pure erosion experiment. The results show that,the entrainment function is not only theoretically well-grounded,ithas a satisfactory accuracy in predicting bed sediment entrainment rates as well. It shows that 87.2% ofthe calculated entrainment rates by the newly obtained entrainment function have a relative error falling in-to the range of [-0.5,0.5],indicating it has a comparatively higher accuracy in comparison with other functions. The entrainment function applied as the bed boundary condition also works well in reproducingthe pure erosion processes. The entrainment function derived in this paper has the advantage over othermethods in that it helps to provide a new approach to statistically associate the dynamic processes of microscopic motion of particles to macroscopic features of sediment transport.