Extended Theory of Hydraulic Hysteresis in Open-Channel Flow

Abstract

The occurrence of hysteresis in a supercritical, open-channel flow approaching an obstacle has been recognized and investigated both experimentally and theoretically over the last few decades. However, the available theory and experimental investigations in the literature do not include the case when subcritical flow, controlled from downstream, can establish across the obstacle. The present work fills this gap by proposing a new theory that includes this occurrence and shows that two different steady flow states can establish for the same obstacle geometry and flow conditions-one with supercritical to subcritical transition far downstream from the obstacle, and the other with supercritical to subcritical transition far upstream from the obstacle. The proposed, more general theory includes the existing theory as a special case. Finally, two specific examples are illustrated and discussed, i.e., the case of flow over a raised bed hump, and the case of flow through a channel contraction.

Positive Surge Propagation in Sloping Channels

“…When a positive surge propagates upstream on a steep slope over an incoming supercritical flow, it progressively decelerates and asymptotically tends toward a stationary hydraulic jump [10]; when, instead, a positive surge propagates upstream on a mild slope over an incoming subcritical flow, the wavefront progressively reduces its height until the surge vanishes. Interestingly, the latter occurrence has never been reported and discussed in the literature and, as it happens, solutions to open channel flow problems never ceases to amaze by showing unexpected behaviours even within simple and schematic frameworks (e.g., [14][15][16][17][18][19][20]).…”

The exact solution to the Shallow water Equations Riemann problem at width jumps in rectangular channels

“…The coexistence of multiple steady states for supercritical flows approaching a contraction is called hydraulic hysteresis (Defina andViero 2010, Viero andDefina 2017). In the early studies (Akers andBokhove 2008, Defina andViero 2010), it was assumed that this phenomenon depended on the upstream flow conditions and on the contraction characteristics, assuming that critical conditions were established at the downstream end of the channel contraction in the flow configurations E1 and E3 (classic hydraulic hysteresis).…”

“…In the early studies (Akers andBokhove 2008, Defina andViero 2010), it was assumed that this phenomenon depended on the upstream flow conditions and on the contraction characteristics, assuming that critical conditions were established at the downstream end of the channel contraction in the flow configurations E1 and E3 (classic hydraulic hysteresis). Viero and Defina (2017) have recently generalized the classic hydraulic hysteresis concept to the case that a subcritical downstream boundary condition may have a role in determining the flow characteristics through the channel contraction (generalized hydraulic hysteresis).…”

“…It is demonstrated that the solution to the Riemann problem always exists, but that there are certain initial conditions for which multiple solutions are possible. In addition, it is shown that the solution multiplicity is connected to the hydraulic hysteresis in contracting channels (Defina andViero 2010, Viero andDefina 2017). Finally, the numerical method by Cozzolino et al (2018b) is analysed, showing that the structure of the algorithm forces the numerical solution with supercritical flow through the width discontinuity when multiple solutions are possible.…”

Comparison between 2D Shallow-Water Simulations and Energy-Momentum Computations for Transcritical Flow Past Channel Contractions

“…There is a vast literature, dating back to Ippen and co-workers [15][16][17], on understanding the mechanics of high-velocity flow in open channels of variable width, with an emphasis on the design of hydraulic structures operating under supercritical conditions (e.g., the design of supercritical channel junctions [18,19] and channel expansions [20]). Recent topics in high-velocity channel flow include the possibility of multiple steady states induced by the complex shock wave interaction in supercritical flow through contractions [21], and the emergence of hysteresis in open channel flow [22,23].…”