Experimental and numerical investigations of the water surface profile and wave extrema of supercritical flows in a narrow channel bend.

Supercritical flows in channel bends, e.g., in steep streams, chute spillways, and flood and sediment bypass tunnels (SBTs), experience cross-waves, which undulate the free surface. The designs of these hydraulic structures and flood protection retaining structures in streams necessitate computing the locations and water depths of the wave extrema. This study numerically and experimentally investigates the water surface profiles along the sidewalls, the wave extrema flow depths, and their angular locations in a narrow channel bend model of the Solis SBT in Switzerland. The 0.2 m wide and 16.75 m long channel has a bend of 6.59 m radius and 46.5° angle of deviation. The tested flow conditions produced Froude numbers ≈ 2 and aspect ratios ranging from 1.14 to 1.83. Two-phase flow simulations were performed in OpenFOAM using the RNG k-ε turbulence closure model and the volume-of-fluid method. The simulated angular locations of the first wave extrema and the corresponding flow depths deviate marginally, within ± 6.3% and ± 2.1%, respectively, from the experimental observations, which signifies good predictions using the numerical model. Larger deviations, especially for the angular locations of the wave extrema, are observed for the existing analytical and empirical approaches. Therefore, the presented numerical approach is a suitable tool in designing the height of the hydraulic structures with bends and conveying supercritical flows. In the future, the model's application shall be extended to the design of the height and location of retaining walls, embankments, and levees in steep natural streams with bends.