Zhu Zhongfan, Hei Pengfei, 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.
College of Life and Environmental Science, Minzu University of China, Beijing 100081, China.
Entropy (Basel). 2020 May 28;22(6):605. doi: 10.3390/e22060605.
The velocity profile of an open channel is an important research topic in the context of open channel hydraulics; in particular, the velocity-dip position has drawn the attention of hydraulic scientists. In this study, analytical expressions for the velocity-dip position over the entire cross section and at the centerline of a rectangular open channel are derived by adopting probability methods based on the Tsallis and general index entropy theories. Two kinds of derived entropy-based expressions have the same mathematical form as a function of the lateral distance from the sidewall of the channel or of the aspect ratio of the channel. Furthermore, for the velocity-dip position over the entire cross section of the rectangular open channel, the derived expressions are compared with each other, as well as with two existing deterministic models and the existing Shannon entropy-based expression, using fifteen experimental datasets from the literature. An error analysis shows that the model of Yang et al. and the Tsallis entropy-based expression predict the lateral distribution of the velocity-dip position better than the other proposed models. For the velocity-dip position at the centerline of the rectangular open channel, six existing conventional models, the derived Tsallis and general index entropy-based expressions, and the existing Shannon entropy-based models are tested against twenty-one experimental datasets from the literature. The results show that the model of Kundu and the Shannon entropy-based expression have superior prediction accuracy with respect to experimental data compared with other models. With the exception of these models, the Tsallis entropy-based expression has the highest correlation coefficient value and the lowest root mean square error value for experimental data among the other models. This study indicates that the Tsallis entropy could be a good addition to existing deterministic models for predicting the lateral distribution of the velocity-dip position of rectangular open channel flow. This work also shows the potential of entropy-based expressions, the Shannon entropy and the Tsallis entropy in particular, to predict the velocity-dip position at the centerline of both narrow and wide rectangular open channels.
在明渠水力学领域，明渠流速分布是一个重要的研究课题；特别是，流速最低点位置引起了水力学科学家的关注。在本研究中，基于Tsallis熵和广义指数熵理论，采用概率方法推导了矩形明渠整个横截面和中心线处流速最低点位置的解析表达式。两种基于熵推导的表达式作为距渠道侧壁横向距离或渠道纵横比的函数，具有相同的数学形式。此外，对于矩形明渠整个横截面上的流速最低点位置，利用文献中的15个实验数据集，将推导的表达式相互比较，并与两个现有的确定性模型以及现有的基于香农熵的表达式进行比较。误差分析表明，Yang等人的模型和基于Tsallis熵的表达式比其他提出的模型能更好地预测流速最低点位置的横向分布。对于矩形明渠中心线处的流速最低点位置，利用文献中的21个实验数据集对六个现有的传统模型、推导的基于Tsallis熵和广义指数熵的表达式以及现有的基于香农熵的模型进行了测试。结果表明，与其他模型相比，Kundu的模型和基于香农熵的表达式对实验数据具有更高的预测精度。除了这些模型外，在其他模型中，基于Tsallis熵的表达式对实验数据的相关系数值最高，均方根误差值最低。本研究表明，Tsallis熵可以很好地补充现有的确定性模型，用于预测矩形明渠水流流速最低点位置的横向分布。这项工作还展示了基于熵的表达式，特别是香农熵和Tsallis熵在预测窄矩形和宽矩形明渠中心线处流速最低点位置方面的潜力。
