Harmonic Function for 3D Warped Transition Geometry and Its Practical Use
Publication: Journal of Irrigation and Drainage Engineering
Volume 148, Issue 6
Abstract
A transition is typically required in irrigation canals, laboratory flumes and many other waterways. The warped type transition (WTT) is the preferred link structure between a small rectangular and relatively large trapezoidal channel section. However, the best method of determining the WTT geometry still requires evaluation. This paper provides an analytical function for the three-dimensional (3D) WTT geometry. This was achieved by solving a Dirichlet problem for Laplace’s equation. The boundary conditions in the problem were chosen based on guidelines and recommendations from earlier studies of transitions. Solving the problem analytically yields a harmonic function. The geometry given by this function guarantees a streamlined rectangular-trapezoidal link and avoids sharp corners. The streamlined transition would work to reduce flow separation and head loss. This paper contributes to the development of a new method for fabricating WTT with precision and repeatability. The harmonic function can generate geometrical data as essential input for laboratory-scale and field-scale WTTs and can aid in the construction of a three-dimensional model for use in computational fluid dynamic models.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This study was funded by the National Sciences and Engineering Research Council of Canada through Discovery Grants held by S. Li. Rui Zeng helped edit the Video_S1.mov file. The author thanks the anonymous reviewers for their helpful comments.
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Received: Jun 4, 2021
Accepted: Jan 11, 2022
Published online: Mar 17, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 17, 2022
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