Computation of 2D Supercritical Free-Surface Flow in Rectangular Weak Channel Bends
Publication: Journal of Irrigation and Drainage Engineering
Volume 150, Issue 5
Abstract
In order to study the supercritical flow in a curved channel of a rectangular cross section, the classical shallow water equations in a cylindrical coordinate system based on the mass and momentum laws that take into account the friction and bottom slope are used. The obtained mathematical model forms nonlinear partial differential equations of first-order. For simplification, a linearization of the partial differential equations (PDEs) set is performed using small perturbation approach valid for weak bends (axial curvature radius extremely larger than the channel width). The governing equations with well-posed initial and boundary conditions were solved for a rectangular bend channel flow by applying the method of characteristics that is capable of transforming the hyperbolic partial differential equations to a system of ordinary differential equations (ODEs). The proposed model is tested and validated by comparing the results with broad available experimental data reported in the literature, and particular attention was paid to the wave maximum and its location. Comparisons indicate a reasonable agreement between the results obtained for the maximum flow depth along the outer channel wall. However, the model prediction is only reliable for a small relative curvature. Despite the model limitations, the results show the reliability and accuracy of the proposed approach for practical design purposes.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the submitted article.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 150 • Issue 5 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Feb 6, 2023
Accepted: Apr 9, 2024
Published online: Jun 17, 2024
Published in print: Oct 1, 2024
Discussion open until: Nov 17, 2024
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