Optimization and Analysis of Advective Travel Times beneath Hydraulic Structures
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 9
Abstract
Steady, 2D Darcian seepage in a homogeneous isotropic porous medium under an impervious structure is studied by the methods of complex analysis. The geometry of the structure is studied focusing on the travel time of a marked (neutral tracer) particle from the upper pool to the tailwater. In the Verigin problem, the angle of inclination of a sheetpile resulting in minimal time along the bounding streamline is . If the maximum of the minimum of the travel time is searched between all streamlines originated in the upper pool, then the optimal angles are found to be and . The minimization of the total volume of fluid that arrives from the upper pool to the tailwater during a prescribed time span is also considered. For arbitrary geometry, structure optimization with respect to travel time is carried out explicitly for the bounding streamline with a constraint on the wetted perimeter of a depressed structure. The minimal-time shape is found to be the Voshinin semicircular structure, which is mathematically generated by a line vortex.
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Acknowledgments
The writer thanks J. R. Craig, O. Satti, F. Marketz, and an anonymous referee for helpful comments and discussions.
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Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 9 • September 2008
Pages: 1311 - 1317
Copyright
© 2008 ASCE.
History
Received: Jan 2, 2007
Accepted: Jan 18, 2008
Published online: Sep 1, 2008
Published in print: Sep 2008
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