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Title: Evaluation of 2D shallow-water model for spillway flow with a complex geometry

Author
item YING, XINYA - UNIVERSITY OF MISSISSIPPI
item WANG, SAM - UNIVERSITY OF MISSISSIPPI

Submitted to: Journal of Hydraulic Research IAHR
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 11/20/2009
Publication Date: 5/7/2010
Citation: Ying, X., Wang, S.S. 2010. Evaluation of 2D shallow-water model for spillway flow with a complex geometry. Journal of Hydraulic Research IAHR. 48:(2)265—268.

Interpretive Summary: The two-dimensional (2D) shallow water model is originally proposed for simulating water flows in the case where the horizontal length scale is much greater than the vertical length scale. Under this condition, the vertical velocity is negligible and vertical pressure gradients are nearly hydrostatic. Recently, as a simple alternative to the complex 3D model, the 2D shallow water model has been increasingly used to compute water flows in the case where these assumptions may be not strictly valid, e.g., flows through spillway chutes as well as overtopping flows through breaches of earthen dams. In order to investigate the applicability of the 2D shallow water model to these types of flows, a 2D numerical simulation of spillway chute flow has been carried out and the computational results are compared with the measured data from the physical model test. The results from this case study show that although the 2D shallow-water model has limitations in accurately predicting discharge capacity and pressure on spillway surface, it can give reasonable prediction of the essential flow features as well as water surface profiles along the chute side walls.

Technical Abstract: Although the two-dimensional (2D) shallow water model is formulated based on several assumptions such as hydrostatic pressure distribution and vertical velocity is negligible, as a simple alternative to the complex 3D model, it has been used to compute water flows in which these assumptions may be not strictly valid, e.g., flows through spillway chutes as well as overtopping flows through breaches of earthen dams. In order to investigate the applicability of the 2D shallow water model to these types of flows, a 2D numerical simulation of spillway chute flow has been carried out and the computational results are compared with the measured data from the physical model test. The numerical model is based on the finite volume method on unstructured triangular grids. The intercell fluxes are evaluated using the HLL approximate Riemann solver. Comparisons between numerical and experimental results demonstrate that the model can correctly capture the essential flow features, such as two shocks behind bridge piers, two oblique standing shock waves due to lateral spillway contraction, and consequent shock-on-shock wave interaction. It is also observed that the computed water surface profiles along the side walls are in good agreement with the measured data from the physical model test. The results from this case study show that although the 2D shallow-water model has limitations in accurately predicting discharge capacity and pressure on spillway surface, it is applicable if the major concern is the downstream chute flow and water depth along the side walls.