Mirauda Domenica, Russo Maria Grazia
School of Engineering, Basilicata University, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy.
Department of Mathematics, Computer Science and Economics, Basilicata University, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy.
Entropy (Basel). 2020 Jun 13;22(6):654. doi: 10.3390/e22060654.
In narrow open channels, the three-dimensional nature of the flow and the transport momentum from the sidewalls to the central region cause the maximum longitudinal velocity to occur below the water surface. The entropy model is unable to accurately describe the velocities near the free surface when the dip phenomenon exists. The present paper proposes a new dip-modified entropy law for steady open channel flows, which consists of three additional terms: the first one similar to Coles' function; the second one linearly proportional to the logarithmic distance from the free surface; and the third one depending on the cubic correction near the maximum velocity. The validity of the new model was tested on a set of laboratory measurements carried out in a straight rectangular flume with smooth boundaries and for different values of water discharge, bottom slope, and aspect ratio. A detailed error analysis showed good agreement with the data measured through the present research and a more accurate prediction of the velocity-dip-position compared with the one evaluated through the original entropy model. In addition, the modified entropy wake law matched very well with other literature data collected in rectangular cross-sections with different flow conditions.
在狭窄的明渠中，水流的三维特性以及从边壁到中心区域的动量传输导致最大纵向速度出现在水面以下。当存在倾斜现象时，熵模型无法准确描述自由表面附近的速度。本文针对稳定的明渠水流提出了一种新的倾斜修正熵定律，它由三个附加项组成：第一项类似于科尔斯函数；第二项与距自由表面的对数距离成线性比例；第三项取决于最大速度附近的三次修正。新模型的有效性在一组实验室测量中得到了验证，这些测量是在具有光滑边界的直矩形水槽中进行的，针对不同的水流量、底坡和宽深比。详细的误差分析表明，与本研究测量的数据吻合良好，并且与通过原始熵模型评估的结果相比，对速度倾斜位置的预测更准确。此外，修正后的熵尾流定律与在不同流动条件下矩形横截面中收集的其他文献数据非常吻合。
