Multiple states in the flow through a sluice gate

Abstract

This paper addresses the problem of hydraulic hysteresis for a supercritical open channel flow approaching a sluice gate when subcritical flow can establish downstream, against the gate. The possible flow configurations across the gate are classified on the basis of the Froude number of the incoming and downstream flows, and of the ratio of gate opening to the upstream supercritical flow depth. Within the above parameter space, two regions exist in which the problem admits a dual solution, that is, two different flow configurations can establish for the same gate opening and undisturbed flow conditions. In one of these regions, both smooth flow (i.e. the fluid flows under the gate without interacting with the gate) and free outflow conditions can establish; in the other region, both smooth flow and submerged flow can establish. For flow conditions in the above regions, the configuration that actually establishes depends on the previous history of the flow, thus implying the hysteretic character of the flow. Journal of Hydraulic Research VieroDefina˙MultipleStatesSluiceGatesupstream flow conditions; the two flow configurations that can occur are (i) the supercritical flow remains supercritical through the obstacle, or (ii) a supercritical to subcritical transition (i.e. a hydraulic jump) occurs upstream of the obstacle, and critical condition establishes at the obstacle. Recently, Viero & Defina (2017) demonstrated that hydraulic hysteresis can occur also when subcritical flow can establish just downstream of, and possibly against an obstacle. In the presence of a downstream subcritical flow against the obstacle, the problem complicates since it has one more degree of freedom (i.e. the downstream flow conditions), and the number of possible flow configurations increases significantly. The two flow configurations that can establish through the obstacle are (i) supercritical smooth flow configuration, i.e. the flow remains supercritical in passing the obstacle and supercritical to subcritical transition occurs downstream of the obstacle; (ii) subcritical smooth flow configuration, i.e. the supercritical to subcritical transition occurs upstream of the obstacle and the flow remains subcritical through (and downstream of) the obstacle. For illustration purposes, Viero & Defina (2017) applied the theory to two specific obstacles, namely a raised bed hump and a channel contraction.By extending the work of Defina and Susin (2003) in the light of the more general framework of Viero & Defina (2017), i.e. the possible presence of a downstream subcritical flow, the present work focuses on the flow through a vertical sluice gate, for which the hysteretic behaviour concerns the possibility that, for a given gate opening, a supercritical approaching flow may either remain supercritical without interacting with the gate, or undergo a supercritical to subcritical transition upstream of the gate, with the flow through the gate that can be either free or submerged depending on the downstream flow conditions. Anyway, the state that ...

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