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Title: Free-surface flow over curved surfaces
Authors: University of Texas at Austin
Berger, Rutherford C.
Keywords: Finite element
Finite element method
Shallow water
Shallow water equations
Mathematical models
Numerical models
Hydraulic structures
Publisher: Hydraulics Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Technical report (U.S. Army Engineer Waterways Experiment Station) ; HL-93-10.
Description: Technical Report
Abstract: Flood flows in excess of a reservoir's capacity must be passed downstream in a manner that does not endanger tbe dam or surrounding hydraulic structures. This is not a trivial task as the flow must fall a great distance to reach the riverbed. These high current velocities coupled with a free surface can easily lead to regions of low pressure in which cavitation may occur or the formation of standing waves and an uneven flow distribution. Poor flow distribution will yield circulation and high velocities at tbe base of the spillway (or outlet channel) known as the "stilling basin," resulting in downstream scour, potentially undermining the structure, causing bank erosion and stilling basin damage. Numerical models of free-surface spillway flows must address high flow velocities and the nonhydrostatic pressure distribution over the curved spillway bed. Common shallow-water models invoke the hydrostatic assumption, and in the case of the St. Venant equations, also the mild-slope assumption and may not be adequate. This investigation develops the equations of a more general shallow-water formulation that includes bed curvature effects. The equations have lateral and longitudinal resolution and an assumed bed-normal velocity distribution. No restriction is placed on the velocity in the plane parallel to the bed. These equations are derived through a singular perturbation analysis in a shallowness parameter. A finite element model is then constructed that represents a discrete version of these equations, and its usefulness is tested in comparison to water surface and pressure measurements gathered in flumes. A Petrov-Galerkin scheme is used in which the degree of modification of the original Galerkin test function is proportional to the eigenvalues, which represent the wave speed. Results with this scheme are compared to those for the standard steep-slope shallow-water equations and the St. Venant equations. The results demonstrate that the new generalized shallow-water equations are a significant improvement over these more conventional equations near the spillway crest and thus in the prediction of the spillway capacity. The St. Venant equations compare more poorly along the spillway face, but this is shown to be a result of the mild-slope assumption, not curvature. Laterally, the new generalized shallow-water equations provide only slight improvement over conventional equations in that the water surface is generally controlled by short-wave phenomena, and these models are all essentially long-wave models. They do provide some qualitative guidance on spillway performance.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Technical Report

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