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Approximate analytical solution for supercritical flow in rectangular curved channels

机译：矩形弯曲通道中超临界流动的近似解析解

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摘要

In this study, we present an asymptotical mathematical model and an analytical solution for a supercritical flow in curved rectangular open channels. An original approach is proposed for solving the free-surface configuration and features of the flow in the presence of cross shock waves. The two-dimensional steady depth-averaged shallow water equations are transformed into an equivalent one-dimensional (1D) unsteady flow problem and a first order approximation is then obtained using small perturbation theory. Furthermore, the 1D asymptotic model is solved analytically by Laplace integral transformation and the two-dimensional flow field solution is reconstructed according to the translating planes. The free-surface profile along the outer chute wall and downstream channel was compared with the available experimental data, and the results indicated the satisfactory agreement of the maximum flow depth, peak positions, and wavelength. The proposed approach provides accurate predictions of the flow features and it facilitates the safe design of curved channel transitions.
机译：在这项研究中，我们提出了曲线矩形明渠中超临界流的渐近数学模型和解析解。提出了一种解决交叉冲击波时自由表面构造和流动特征的原始方法。将二维稳态深度平均浅水方程式转换成等效的一维（1D）非恒定流问题，然后使用小扰动理论获得一阶近似值。此外，通过拉普拉斯积分变换对一维渐近模型进行解析求解，并根据平移平面重建二维流场解。将沿外溜槽壁和下游通道的自由表面轮廓与可用的实验数据进行了比较，结果表明最大流动深度，峰位置和波长令人满意。所提出的方法提供了对流动特征的准确预测，并且有助于弯曲通道过渡的安全设计。

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  • 来源
    《Applied Mathematical Modelling》 |2020年第4期|191-203|共13页
  • 作者

  • 作者单位

    Department of Civil Engineering and Hydraulics Faculty of Science and Technology. University of Jijel Ouled Aissa 18000 Jijel Algeria;

    Laboratory of Applied Hydraulics and Environment (LRHAE) Department of Hydraulics Faculty of Technology University of Bejaia Targa Ouzemour 06000 Bejaia Algeria;

    Research Laboratory in Subterranean and Surface Hydraulics (LARHYSS) University of Biskra 07000 Biskra Algeria;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Analytical solution; Channel transition; Curved channel; Laplace transform; Standing waves; Supercritical flow;

    机译：分析溶液;频道转换;弯曲通道拉普拉斯变换驻波;超临界流;

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