Multiple States In Open Channel Flow
Free (open access)
A. Defina & F.M. Susin
Steady flow regimes in a free surface flow approaching an obstacle are described and extensively discussed. Attention is focused on the phenomenon of hydraulic hysteresis, and a simple one-dimensional theory to predict its occurrence in a supercritical channel flow is proposed. It is shown that in many cases knowledge of the Froude number of the undisturbed approaching flow and of a geometric characteristic of the obstacle allows for a reliable prediction of the flow state. In the region of multiple regimes, however, the previous history of the flow must also be known. Three different obstacles in a rectangular channel are considered, namely a sill, a vertical sluice gate, and a circular cylinder, and the theoretical boundaries of the hysteresis region are specified for each obstacle. The experimental results show that the theoretical predictions are consistent with experiments in the case of obstacles that do not affect channel width (i.e. sills and gates). On the contrary, in the case of channel contraction, a further parameter, which the presented theory does not account for, was found to affect the behavior of the flow, namely the ratio of undisturbed flow depth to contraction width. Finally, in the case of a vertical sluice gate it was found that hysteresis develops in a subcritical undisturbed approaching flow as well. 1 Introduction The occurrence of steady rapidly varied flow in the vicinity of short obstacles is not unusual in open channels. Prediction of flow characteristics as a function of undisturbed approaching flow conditions and obstacle geometry is a primary objective, mainly related to design purposes. In fact, this information must usually be known in order to establish whether or not a constriction is severe enough to influence the upstream flow and to accurately estimate any possible increase in flow depth upstream of the obstacle.