Optimization and Analysis of Advective Travel Times beneath Hydraulic Structures

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 π∕2 . 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 0.404π and 0.596π . 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...