EXACT ANALYTICAL SOLUTION FOR SUPERCRITICAL FLOW IN RECTANGULAR CURVED CHANNELS

Abstract

The present work deals with the mathematical modelling and analytical solution of the problem of standing waves in rectangular curved channels under supercritical flow regime. To date, several numerical models and some analytical solutions have been proposed, however the restrictions and complexities of these models developed during the last decades lead to an increased need for a simple and reliable tool for practical use. Using the perturbation method in power series of the relative curvature, the curvilinear 2-D Saint-Venant’s equations have been reduced to a linear form. The analytical solution of the non-homogeneous wave equation was obtained by the D'Alembert method after adding the boundary conditions. The validation of the proposed solution was made on the case of a curved channel where it was a question of predicting the configuration of the free surface in a rectangular cross-section profile. The data used as a test come from the experiences of Ippen (1936), Poggi (1956) and Beltrami et al. (2007) and the results were very satisfactory for this purpose compared to the experimental measurements.