Author(s): Aida Mnasri; Ezzeddine Hadj Taieb
Linked Author(s):
Keywords: Open channel flow; Transient flow; Prismatic channel; Finite element method; Uniform flow
Abstract: In this paper, consideration is given to the finite element method solution of transient flows in prismatic open channels. In order to improve the understanding of this phenomenon, a mathematical formulation based on one-dimensional Saint-Venant equations is presented to describe free surface wave propagations in open channels. The governing equations for such motion are two coupled non-linear, hyperbolic, partial differential equations of first order. Since the governing equations are non-linear, the solution of the equation system can be obtained only by some approximate numerical techniques. The finite element method, based on the Galerkin formulation, is applied to discretize the mathematical equations leading to a non-linear system of equations solved by an iterative Gauss substitution method. The application relates to the case of a free surface transient flow in prismatic channel (rectangular, triangular and trapezoidal). The transient regime is caused by the opening of a valve located downstream of the channel, the upstream end being connected to a constant level reservoir. In this case, the transient flow represents an evolution between two uniform steady states: initial with zero flow and final at a constant flow equal to those imposed by the valve opening. The uniform flow is defined by Manning formula. The results concern the evolution of hydraulic parameters, depths and discharges, in different sections of the channel, following the downstream maneuver. They were used to analyze the propagation and reflection of surface waves on both ends of the channel. Especially, the numerical results show that when bed width of the channel is very small (the case of the triangular section) depths fluctuations are rapidly damped. To validate the reliability of the model presented herein, the numerical results are compared, in the case of trapezoidal channel, with those of other authors obtained by the method of characteristics.
Year: 2013