Steady supercritical flow in a straight-wall open-channel contraction

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

“…The 2D shallow water theory predicts a complex pattern of oblique standing waves, while the 1D theory yields gradually varied supercritical flow throughout. The experimental observations reveal a water surface that is smoother than our 2D simulations, a feature that seems to be better described by 3D simulations [44]. Qualitatively, both the 1D and 2D models capture the overall water surface profile along the centerline.…”

“…In Figure 5b we show the comparison between the recent experimental observations of [44] and our 1D and 2D model predictions. For the 1D computations we construct the 1D water profile by integrating Equations (1) and (2) forward from the inlet section, with initial condition h = 0.03 m. For the 2D SWE, we impose supercritical inlet boundary conditions based on the known depth and total discharge, Q = 0.041 m 3 /s, and supercritical flow at the outlet.…”

“…In this section we consider the experimental set-up proposed by Ippen and Dawson [16], which has been used as a benchmark for models of high-velocity open channel flow over the past few decades [32,41,42,44]. The flume geometry and basic flow features (illustrated by the steady-state water depth predicted by the 2D SWE) are shown in Figure 5a.…”

“…Figure 6 shows the 1D and 2D predictions using several values of the Manning coefficient (n = 0.011, 0.01, 0.0075 and 0.005). Note that the experiments were conducted in a Plexiglass flume [44], for which n ∼ 0.01 seems appropriate. Small values of the friction coefficient lead to a nearly constant water depths downstream of the contraction, which are significantly smaller than the observed ones.…”

“…Flow simulators based on the SWE have been benchmarked against analytical solutions [30,31], small scale laboratory experiments [30,[32][33][34][35][36][37], and well documented field-scale cases [38][39][40]. Channel transition problems have extensively been simulated using the 2D SWE, with particular emphasis on the effect of channel contractions on the propagation and reflection of surface waves [30], the comparison between simulations and experiments [32,[41][42][43], and the generation of oblique standing waves induced by the channel geometry under supercritical flow conditions [32,37,44].…”