Curved spillway with ceiling flow

Abstract

~en placing deep spillways in a concrete dam it is often necessary to turn their axis in the vertical plane.It is easy to accomplish such turning in pressure spillways with the main regulating gates installed near the outlet section.The deep spillways of the Midori dam (Japan), Castelo do Bode dam (Portugal), etCo, can serve as examples of using such spillways in world hydrotechnical construction practice.However, the use of pressure spillways is far from always the economically most advantageous design. This is due to the need to create on the downstream face of the dam the main gates (usually radial), their hoisting gear, rooms for the latter, access tracks, etc.The steeper the do~mstream face of the main profile of the dam, the more noticeable these difficulties become.If it is proposed to create a spillway with a free-flow regime and regulating gates in the inlet part, which is usually extremely desirable, then specialists are faced with a number of restrictions.These restrictions are primarily due to the provision of flow on the bottom without separation and the absence of cavitation~We can show that, having analyzed the position of the free flight of the jet relative to the downstream face of the dam (Fig. la), solving simultaneously the equations of the trajectory of free fall of the jet ~=x~g~+x2/4{p2cos2~ll(1) and outline of the downstream face V=xfga--H,we find the location of the point of contact of the curve and slope (point K in Fig. la).In the general case(2) 2H xK--tga--tg$ ' \f tg~.--tg~2tg~ ---1). 9K= H (3) When ~ = 0, tan ~ = i/~, then XK=2q'H, !IJ~=H.An analysis of the interrelation of angles B and a (see Fig. Ib) shows that the more "well-proportioned" the dam, the greater the value of the angle of entry ~ that must be specified so that the flow along the bottom without a discontinuity of the surface could join with the do~stream face of the dam.If for gravity dams on a rock foundation, where usually a = 53-57 ~ [i], the angles of entry vary approximately from i0 ~ to 20 ~ (see Fig. ib), then for gravity-arch and especially for gravity dams, where a ~ 60 ~ angle B reaches 30~ ~ Inlet structures with such entry angles are rarely used in hydrotechnical construction and are considered poorly designed.If we consider that ~ = 45 ~ is the maximum value of the angle, then in dams with a < 67o30 ' the construction of a free-flow spillway with flow along the bottom becomes simply impracticable.Another substantial restriction of using such spillways is the low degree of using the head created by the dam (see Fig~ Ic).This circumstance can entail an unjustified increase in the number or size of the spillway outlets.It follows from the graph in Fig. ic that if with the use of a free-flow spillway in a dam with a slope angle of the downstream face ~ = 50 ~ only half of the head can be used, then when a = 65 ~ only about one-third of the head created by the dam can be used.Taking into account that the heights of modern concrete dams reach more than 200 m [i] have been developed and are being introduced [2],...