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

Abstract

Multidimensional simulators of channel and river flow are widely used in industry and academia, raising the question about whether the classical one-dimensional theory of open-channel flow remains relevant in hydraulic engineering. Channel contractions that induce transcritical flow are interesting scenarios to test the classical 1D theory against multidimensional simulations, because supercritical flow in channels of variable width leads to multidimensional flow structures. Transcritical flows are important in practice, because the ensuing hydraulic jumps and regions of supercritical flow may damage hydraulic structures that otherwise operate under tranquil conditions. We compare well-resolved simulations of the 2D shallow-water Equations (SWE) with 1D energy-momentum calculations for flow past symmetric channel contractions. We analyze the accuracy of the classical energy-momentum gradually-varied flow theory to predict the onset of regime transitions and the location of hydraulic jumps. We test the relative performance of the 1D theory for different constriction geometries, and identify the flow mechanisms behind the discrepancies between the 1D and 2D predictions. The grid resolution used in the 2D SWE plays an important role in these predictions, because coarse-grid 2D simulations yield essentially quasi-1D results. Considering its simplicity and negligible computational cost compared with the 2D SWE simulations, the classical 1D theory performs remarkably well for a wide range of flow conditions and contraction geometries. In contrast, we observe large deviations between the 1D and 2D models in flow past abrupt contractions with a large width ratio, as expected. Only modified versions of the 1D theory, taking into account intense local head losses and the propagation of spatial flow structures downstream from the contraction, can succeed at describing these flow scenarios.