Design of Channel Curves for Supercritical Flow

Characteristics of flows around curved sections of open channels at velocities greater than the wave velocity (that is, F > 1) are discussed in this paper. In simple curves such flows produce cross-wave disturbance patterns which also persist for long distances in the downstream tangent. These disturbance patterns indicate nonequilibrium conditions whose basic cause (when F > 1) is that disturbances cannot be propagated upstream or even directly across the channel. Thus, the turning effect of the curved walls does not act equally on all filaments in a given cross section and equilibrium is destroyed. The paper outlines two basic methods of eliminating these disturbance patterns. Analytical design criteria are developed, and experimental verifications of the analyses are presented. The first method consists of applying a lateral force in such a way that it acts simultaneously on all filaments, causing the flow to turn without disturbing the equilibrium. Bottom banking supplies such a lateral force, and a series of vertical curved vanes across the channel has roughly the same effect. The second method employs interference patterns introduced deliberately at the beginning and at the end of the curve. Compound curves, spiral transitions, and sills all operate on this principle. Rectangular channels are uniquely suited to the interference method of treatment, since for a given channel the wave patterns are substantially independent of the flow. Trapezoidal and other nonrectangular channels should be avoided if possible, unless the flow is invariant. The fields of application of the different treatments are discussed briefly