Sur une méthode numérique de calcul des écoulements non permanents soit à surface libre, soit en charge, soit partiellement à surface libre et partiellement en charge

On a numerical method for calculations of free-surface, or pressurized, or partially free-surface and partially pressurized unsteady flow

Institut de mécanique de Grenoble, B.P. 53X, 38041 Grenoble Cedex, France

Abstract

The fluid is submitted to gravity and is compressible while the conduit is elastic or not. The equations are those of continuity, of momentum, of fluid compressibility and eventually of pipe elasticity. From a state of flow at t = n * Δt, we suppose a regim (submerged or not) at each section at t = (n + 1) * Δt. Taking into consideration the variations of height or pressure derived from these assumptions, we calculate a state of flow that will be the state of flow at t = (n + 1) * Δt if the calculated regims agree with the supposed regims. The method is used to determine the water-hammer in a channel bounded by a wall at one end and by a ceiling, and the partially free-surface, partially pressurized flow in a pipe.