Flow in Spillways with Gradually Varied Curvature

Abstract

In the conventional design of a spillway invert and flow bucket, circular, elliptic, and parabolic curves are generally used to connect straight boundaries. Because of the abrupt change in curvature at tangency points, considerable drop of pressure may occur, which sometimes causes cavitation damage. Two kinds of curves with gradually varied curvature, CGVC 1 and CGVC 2, are suggested in spillway design to connect two given points. The slope and the curvature at both ends are specified for a CGVC 1 curve. For a CGVC 2 curve, with other conditions the same as CGVC 1, the curvature at the downstream end is not prescribed. A variable domain finite element scheme, in which the location of the free surfaces of the jet is determined simultaneously with the stream function, is then briefly described. The proposed curves with gradually varied curvature are used in four sample designs. Computational results with the finite element scheme indicate that the new designs give better pressure distribution than the conventional one.