Zhu Zhongfan, Yu Jingshan, Dou Jie, Peng Dingzhi
Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China.
Department of Civil and Environmental Engineering, Nagaoka University of Technology 1603-1, Kami-Tomioka, Nagaoka 940-2188, Japan.
Entropy (Basel). 2019 May 23;21(5):522. doi: 10.3390/e21050522.
In the context of river dynamics, some experimental results have shown that particle velocity is different from fluid velocity along the stream-wise direction for uniform sediment-laden open-channel flows; this velocity difference has been termed velocity lag in the literature. In this study, an analytical expression for estimating the velocity lag in open-channel flows was derived based on the Tsallis entropy theory together with the principle of maximum entropy. The derived expression represents the velocity lag as a function of a non-dimensional entropy parameter depending on the average and maximum values of velocity lag from experimental measurements. The derived expression was tested against twenty-two experimental datasets collected from the literature with three deterministic models and the developed Shannon entropy-based model. The Tsallis entropy-based model agreed better with the experimental datasets than the deterministic models for eighteen out of the twenty-two total real cases, and the prediction accuracy for the eighteen experimental datasets was comparable to that of the developed Shannon entropy-based model (the Tsallis entropy-based expression agreed slightly better than the Shannon entropy-based model for twelve out of eighteen test cases, whereas for the other six test cases, the Shannon entropy-based model had a slightly higher prediction accuracy). Finally, the effects of the friction velocity of the flow, the particle diameter, and the particles' specific gravity on the velocity lag were analyzed based on the Tsallis entropy-based model. This study shows the potential of the Tsallis entropy theory together with the principle of maximum entropy to predict the stream-wise velocity lag between a particle and the surrounding fluid in sediment-laden open-channel flows.
在河流动力学背景下，一些实验结果表明，对于均匀含沙明渠水流，沿流向方向颗粒速度与流体速度不同；这种速度差异在文献中被称为速度滞后。在本研究中，基于Tsallis熵理论并结合最大熵原理，推导了一种估算明渠水流中速度滞后的解析表达式。推导得到的表达式将速度滞后表示为一个无量纲熵参数的函数，该参数取决于实验测量中速度滞后的平均值和最大值。利用三个确定性模型和所建立的基于香农熵的模型，对从文献中收集的22个实验数据集对推导得到的表达式进行了检验。在总共22个实际案例中的18个案例中，基于Tsallis熵的模型比确定性模型与实验数据集的吻合度更好，并且这18个实验数据集的预测精度与所建立的基于香农熵的模型相当（在18个测试案例中的12个案例中，基于Tsallis熵的表达式比基于香农熵的模型吻合得稍好，而在其他6个测试案例中，基于香农熵的模型具有稍高的预测精度）。最后，基于Tsallis熵的模型分析了水流的摩阻流速、颗粒直径和颗粒比重对速度滞后的影响。本研究表明了Tsallis熵理论与最大熵原理在预测含沙明渠水流中颗粒与周围流体之间流向速度滞后方面的潜力。
